LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

GIFT  OK 


Class 


Relations  between  Length,  Elasticity, 

and  Magnetization  of  Iron 

and  Nickel  Wires. 


DISSERTATION. 


SUBMITTED  TO  THE  BOARD  OF  UNIVERSITY  STUDIES  OF  THE  JOHNS 

HOPKINS   UNIVERSITY,  FOR   THE    DEGREE  OF 

DOCTOR  OF  PHILOSOPHY, 


BY 


EDSON   F.  GALLAUDET. 


1.896. 


WASHINGTON,  D.   C.  '. 

GIBSON  BROS.,  PRINTERS  AND  BOOKBINDERS. 


It  has  long  been  known  that  magnetic  metals  change  their  di- 
mensions when  magnetized.  Begun  by  Joule7,  the  study  of 
these  changes  has  taken  the  attention  of  many  careful  investiga- 
tors, whose  work,  especially  that  of  Bidwell3,  has  established  the 
following  facts  with  regard  to  the  phenomena  observed. 

HISTORICAL  SUMMARY. 

Iron. — If  subjected  to  an  increasing  magnetic  field,  iron  at 
first  elongates  in  a  direction  parallel  to  the  direction  of  its  mag- 
netization, more  rapidly  than  in  proportion  to  the  magnetizing 
field,  reaches  a  maximum  length,  and  then  contracts  nearly  in 
proportion  to  the  magnetizing  field,  to  less  than  its  original 
length.  As  the  strength  of  the  field  is  greatly  increased,  the 
contraction  shows  signs  of  reaching  a  limit,  which  was  reached 
by  one  of  Bidwell's311  specimens  at  about  H  =  1250. 

The  absolute  value  of  the  change  in  length  varies  with  different 
specimems,  but  is  qualitatively  the  same  in  all.  If  tension™1 12  is 
applied  to  the  iron,  the  initial  elongation  is  decreased,  and  a 
great  enough  tension  destroys  it  entirely,  making  the  initial 
phenomenon  a  contraction. 

Hardening^1 12  decreases  the  elongation,  and  increases  the  con- 
traction. 

Annealing3f  also  diminishes  the  initial  elongation,  and  increases 
the  final  contraction. 

Nickel  is  found,  by  Bidwell,  to  contract  from  the  start,  ap- 
proaching a  minimum  length  rather  sooner  than  iron,  i.  e.,  at 
about  If=  900  c.  g.  s.,  for  a  particular  specimen311. 

Tension3'1  diminishes  the  contraction  in  weak  fields.  In  fields 
of  strength  greater  than  140  or  150,  magnetic  contraction  is  in- 
creased by  tension,  up  to  a  critical  value,  depending  on  the 
strength  of  the  field,  and  diminished  by  greater  tension. 

FAULTS  OF  PREVIOUS  WORK. 

In  all  but  one13"  of  the  investigations  made  prior  to  last  winter, 
a  relation  between  change  in  length  and  magnetizing  field  only 


144002 


has  been  given.  This  fact  led  last  year  to  the  investigation  of 
Dr.  More1-  in  this  laboratory,  who  got  curves  between  change  in 
length  of  an  iron  wire  and  magnetization. 

In  order  to  get  the  change  in  length  due  to  the  magnetization 
alone,  he  considered  the  metal  as  under  a  mechanical  stress 8  equal 

T>2 

to        ,  and  therefore  having  suffered  a  purely  mechanical  con- 

O7T 

J52 

traction  proportional  to  6- .     He   therefore   measured  Young's 

O/T 

modulus,  and  the  induction  J5,  deduced  this  mechanical  contrac- 
tion, and  added  it  with  positive  sign,  to  his  curves  between 
change  in  length,  and  /  the  magnetization.  It  was  known  that 
Young's  modulus4' l5  for  iron  changed  when  the  iron  was  mag- 
netized, but  Dr.  More  showed  that  he  could  neglect  the  small 
correction  due  to  this  cause,  when  the  tension  in  the  wire  was 
small.  His  curves  for  the  wire,  under  the  minimum  tension  used, 
are  given  below.  The  upper  one  is  intended  to  show  the  rela- 
tion between  change  in  length  and  magnetization  alone,  and  is 

j> 
obtained  by  applying  the  g-  correction  to  the  lower  one,  which 

is  the  uncorrected  relation  as  observed.  Both  curves  show  that 
as  the  magnetization  increases,  the  length  increases,  at  first 
slowly,  then  more  rapidly,  reaching  a  maximum  shortly  before 
saturation,  when  the  wire  begins  suddenly  to  contract  quite 

rapidly,  and  the  curve  falls  in  an  almost  vertical  straight  line. 

jfi 
The        correction  merely  raises  the  curve,  without  changing  its 

o~ 

general  shape.  There  is,  however,  considerable  doubt :>l>  as  to 
the  propriety  of  this  correction. 

The  careful  work  of  Bidwell  principally,  and  the  results  to  be 
given  presently,  show  that  the  contraction  of  iron,  after  satura- 
tion is  reached,  is,  for  a  time  at  least,  proportional  to  the  mag- 
netizing force. 

Bidwell's  experiments  with  very  strong  fields  "'  also  show  that 
the  contraction  approaches  a  limiting  value  asymptotically.  In 
other  words,  the  retraction  curve,  after  saturation,  is  first  a  de- 
scending straight  line,  and  then  becomes  curved  with  its  concave 

I  > 

side  upward.     The  curve  of         plotted  to  //,  constantly  rises,  but 

~ 


is  convex  upward  where  the  retraction  curve  is  straight,  and  con- 
cave upward  where  the  inductions  are  large.  If,  therefore,  that 
part  of  the  change  in  length,  which  is  not  due  to  the  magnetiza- 

J52 

tion,  were  a  contraction  proportional  to  ^— ,  the  contraction  that 

immediately  follows  saturation,  should  be  less  than  proportional 
to  the  field ;  i.  e.,  that  part  of  the  contraction  curve  that  imme- 
diately follows  saturation,  should  be  concave  upward,  while  ex- 
periment shows  it  to  be  straight.  Also,  for  very  strong  fields, 

J?2 

the  rapid  increase  in  -  —  should  make  the  contraction  more  rapid 

than  in  proportion  to  the  field  ;  i.  e.,  the  contraction  curve  should 
finally  curve  downward.  The  work  of  Bid  well,  already  cited, 
shows  the  reverse  to  be  the  fact.  Finally,  if  the  change  in  length 

were  due  to  change  in  I  and  in  £— ,  Dr.  More's  curve,  as  cor- 
rected, should  come  to  an  end  at  a  point  given  by  the  maximum 
elongation  as  ordinate,  and  maximum  magnetization  as  abscissa. 
In  reality  his  curve  falls  almost  perpendicularly  just  before  reach- 
ing the  point  where  it  should  end,  showing  that  after  the  metal 
is  nearly  saturated,  the  change  in  length  is  independent  of  both 

JM 

the  magnetization  and  of  — .     It  seems,  therefore,  reasonable  to 

J52 

assume  that  the  change  in  length  is  also  independent  of  ^-  before 

o/r 

this  point  is  approached. 

OBJECT  OF  INVESTIGATION. 

The  following  investigation  was  undertaken  at  the  suggestion 
of  Dr.  Ames,  with  the  original  purpose  of  studying  iron,  nickel, 
cobalt,  and  bismuth,  and  in  the  hope  that  a  tabulation  of  Young's 
modulus,  along  with  induction,  permeability,  field  strength,  and 
magnetization,  as  well  as  the  change  in  length  of  each,  would 
show  enough  connection  between  some  of  these  quantities,  to 
explain  the  phenomena.  It  was,  however,  impossible  to  get  bis- 
muth and  cobalt  in  the  form  of  wire ;  hence  the  investigation  is  con- 
fined to  iron  and  nickel.  Also,  on  account  of  the  many  set-backs 
in  getting  the  apparatus  to  work  satisfactorily  in  its  necessary 
surroundings,  and  owing  to  the  short  time  available,  it  has  been 


•  6 

possible  to  investigate  only  one  specimen  of  each  metal.  This  is 
especially  to  be  regretted,  since  the  results  differ  unexpectedly, 
and  in  an  important  manner  from  any  given  by  previous  investi- 
gators. 

DESCRIPTION  OF  APPARATUS  AND  METHOD  OF  OBSERVATION. 

The  apparatus  was  the  same  as  that  used  by  Dr.  More  last 
year,  and  is  shown  in  figures  1  and  2.  The  wire  was  encased  in  a 
brass  tube  a,  Fig.  1,  open  at  the  upper  end  and  closed  at  the  lower 
end  by  a  brass  plug  b.  At  the  top  was  a  bracket  c  supporting  a 
lever  d,  and  a  projecting  arm  e.  The  wire  experimented  on 
passed  up  through  the  brass  plug  b,  in  which  it  was  tightly 
fastened  by  a  set-screw,  was  held  concentric  in  the  tube  by  a 
loosely-fitting  cork/,  in  the  open  end  of  the  tube,  carried  tightly 
screwed  to  it  immediately  above  the  cork,  a  brass  hook  g,  and 
finally  passed  to  the  support  above,  thus  carrying  the  load  of 
the  tube  and  bracket.  The  hook  g,  screwed  to  the  wire,  made  a 
knife-edge  connection  with  the  short  arm  of  the  lever  f?,  which 
was  supported  on  knife  edges  by  the  bracket  c. 

The  projecting  arm  e  of  the  bracket  passed  out  under  and 
parallel  to  the  long  arm  of  the  lever  d,  and  had  its  extremity 
bent  up,  so  that  this  extremity  and  the  upper  surface  of  the  end 
of  the  lever  lay  near  together  and  in  the  same  plane  when  at 
rest.  A  small  brass  table  h  furnished  with  three  legs  made  of 
needle  points  about  3  mm.  apart,  was  placed  on  the  end  of  the 
lever,  so  that  two  of  its  legs  rested  in  a  scratch  in  the  lever, 
while  the  third  leg  rested  on  the  raised  extremity  of  the'project- 
ing  arm  of  the  bracket.  This  little  three-legged  table  carried  a 
bit  of  plane  glass  mirror,  in  which  a  vertical  scale  was  observed 
by  means  of  a  telescope.  It  is  evident  that  any  change  in  the 
length  of  the  part  of  the  wire  between  the  set-screws  in  the  plug 
b  and  the  hook  #,  must  change  the  inclination  of  the  lever  d  and 
tilt  the  mirror  at  h. 

If 

L  =  length  of  long  arm  of  lever, 
/  =  length  of  short  arm  of  lever, 
d  =  distance  from  one   leg  of  brass  table  to  line  joining  other 

two  bearing  on  lever  end, 
D  —  distance  from  scale  to  mirror, 


I                 ! 

i 

i 

i 

? 

i        i 

i 

i 

| 

i        i 

1                 1 

i 

1 

bH 

i           ; 

1                 1 

i 

1 

i            i 

1                 1 

i 

1                 1 

Ui  i 

i 

UI  i 

LJ 

i            i 

1                 1 

i 

i           i 

!               F 

I 

then  the  multiplying  power  of  the  apparatus  is 

X  2 


Z  =  11.67  cm.     J  =  0.477     d  =  0.3365     D  =  147.6 

therefore  multiplying  power  is 

11.67  X  147.6  X  2  _        ^ 
All  X  .3365 


Hence  Scalre  §'ives  the  actual  changes  in  the  length  of 


the  wire.  It  was  possible,  under  good  conditions,  to  read  the 
scale  to  one-tenth  of  a  millimeter,  corresponding  to  an  actual 
change  in  length  of  0.000000466  cm.  The  length  of  the  wire 
between  fastenings  =  70  cm.  It  was  therefore  possible  to  de- 
tect, with  a  fair  degree  of  certainty,  changes  in  the  unit  length 
as  small  as  0.000,000,006,6,  or  one  part  in  150,000,000. 

The  hollow  brass  tube  a,  containing  the  wire,  and  supported 
by  it,  was  placed  inside  a  vertical  solenoid  a,  Fig.  2,  considerably 
greater  in  length  than  the  tube  itself,  thus  bringing  the  set- 
screws  in  b  and  y,  Fig.  1,  well  within  the  magnetic  poles  of  the 
wire  studied.  The  wire  of  the  solenoid  was  wound  on  a  brass 
tube,  inside  which  another  brass  tube  was  placed,  thus  forming 
a  jacket  between  the  wire  of  the  coil  carrying  the  magnetizing 
current,  and  the  suspended  tube  containing  the  specimen  studied. 
A  stream  of  cold  water  was  kept  flowing  in  this  jacket,  so  that  it 
took  some  time  for  the  heating  of  the  current  to  affect  the  read- 
ing in  the  telescope.  The  strength  of  the  field  was  45.7  c.  g.  s. 
per  ampere.  For  weak  fields  the  magnetizing  current  was  meas- 
ured by  a  Weston  mil-ammeter,  and  regulated  by  a  water  and 
copper  sulphate  resistance.  For  strong  fields,  the  current  was 
measured  by  a  Weston  ammeter  of  greater  capacity,  reading  to 
hundredths  of  an  ampere,  and  was  regulated  by  an  iron  wire  re- 
sistance. The  current  was  obtained  from  the  storage  cells  of 
the  laboratory,  and  could  be  kept  very  constant. 

The  induction  in  the  wire  was  measured  by  the  method  of  in- 
creasing reversals. 

In  the  case  of  the  iron,  a  paper  cylinder,  wound  with  two 
hundred  turns  of  fine  copper  wire  connected  with  a  Rowland- 


d'Arsonval  galvanometer,  was  slipped  over  the  wire,  and  placed 
midway  between  the  ends  of  the  tube  a,  Fig.  1. 

For  the  nickel,  instead  of  using  the  paper  cylinder,  a  thin 
coating  of  sealing-wax  was  first  applied,  over  which  were  wound 
four  hundred  turns  of  fine  silk-covered  wire,  connected  with  the 
galvanometer.  After  each  set  of  induction  measurements,  the 
galvanometer  was  calibrated  by  means  of  a  long  solenoid  wound 
on  a  wooden  core,  and  carrying  a  secondary  coil  of  two  hundred 
turns.  The  mean  area  of  the  secondary  coil  upon  the  wire  was 
carefully  measured  and  the  section  of  the  wire,  whence  the  in- 
ductions were  calculated  in  the  usual  manner. 

The  lower  end  of  the  wire  studied,  was  provided  with  a 
weight-carrier  £,  Fig.  2,  so  that  weights  could  be  added  and 
measurements  taken  of  Young's  modulus.  The  stretching 
weight,  or  rider  c,  weighing  46.9  grams,  consisted  of  a  piece  of 
brass  tubing  about  3  cm.  in  diameter,  and  the  same  in  length. 
One  side  was  cut  axially,  so  that  it  could  be  applied  without  re- 
moving the  weight-carrier.  Two  loops  of  copper  wire  were 
soldered  to  opposite  sides  of  this  rider,  and  through  these  passed 
light  wire  hooks  suspended  by  strings  which  passed  through  two 
small  pulleys,  one  on  each  side  of  the  stretched  wire,  and  about 
1.5  cm.  from  it.  Above  the  pulleys  the  strings  were  united  into 
a  single  one  d,  and  carried  to  the  table  where  the  readings  were 
taken,  and  there  fastened.  The  length  of  this  string  was  such 
that  when  it  was  fully  extended,  the  rider  was  supported  by  the 
weight-carrier,  and  the  supporting  hooks  just  swung  free  of  the 
side  loops.  When  it  was  desired  to  remove  the  rider,  the  string 
d  was  drawn  aside,  and  held  by  a  tack  in  the  table,  which  kept 
the  rider  freely  suspended,  about  3  mm.  above  the  weight- 
carrier. 

Great  difficulty  was  experienced  in  getting  trustworthy  results 
from  an  apparatus  of  such  delicacy.  The  induction  measure- 
ments could  be  made  at  any  time,  but  the  length  and  modulus 
measurements  had  to  be  made  between  two  and  four  in  the 
morning,  when  the  traffic  of  the  city  was  less  than  at  any  other 
time,  and  even  then,  the  effect  of  the  March  winds  upon  the 
building  was  a  sore  trial  to  the  patience.  A  very  important 
source  of  error  was,  of  course,  found  to  be  that  due  to  the  heat- 
ing of  the  current  in  the  coil.  It  was  finally  found  necessary 


to  read  only  instantaneous  changes  of  length,  both  for  the  elon- 
gation curve,  and  for  the  change  in  Young's  modulus. 

In  measuring  Young's  modulus  there  seemed  to  be  an  instan- 
taneous elongation  upon  applying  the  rider,  followed  more  or 
less  continuously  by  a  slow  increase  in  the  reading,  showing  an 
apparent  viscosity  of  the  metal.  On  account  of  the  heating,  it 
was  impossible  to  wait  for  the  modulus  reading  to  become  con- 
stant, but  the  instantaneous  elongation  was  guessed  at  as  nearly 
as  possible  and  though,  of  course,  much  too  small  to  give  the 
usual  value  of  Young's  modulus,  and  also  too  irregular  to  be  of 
any  quantitative  value,  was  still  near  enough  what  it  should 
have  been  to  show  the  approximate  position  of  the  modulus 
curve.  In  any  case,  whatever  the  modulus  curve  may  be,  the 
elongation  and  retraction  curve  seems  to  be  independent  of  it, 
so  that  accuracy  in  this  respect  is  not  vital.  It  was  also  the  ex- 
ception to  have  the  apparatus  free  from  vibrations,  though  its 
supports  rested  in  boxes  of  sawdust  e,  Fig.  2,  and  the  whole  was 
placed  on  brick  piers  built  up  from  the  ground.  But  fortunately 
the  night  on  which  the  first  iron  curve  was  taken  was  unusually 
quiet,  and  all  the  conditions  most  favorable,  as  the  results  seem 
to  show,  since  a  smooth  curve  can  be  drawn  through  nearly  all 
the  points  obtained.  The  wires  were  annealed  before  being  set 
up,  and  demagnetized  by  an  alternating  current  before  each  set 
of  measurements. 

The  elongation  curves  were  taken  as  follows  :  A  reading  was 
taken  through  the  telescope,  the  magnetizing  current  then  in- 
creased a  small  amount,  and  another  reading  taken  immediately. 
The  process  was  then  repeated  without  turning  off  the  current, 
and  carried  from  zero  current  to  between  6  and  7  amperes,  or  a 
field  of  about  300.  [The  current  had  to  be  turned  off  twice  dur- 
ing each  set  of  measurements,  to  allow  a  change  in  the  voltage 
applied,  which,  on  account  of  high  resistance  of  the  solenoid  and 
the  low  resistance  of  the  rheostats  obtainable,  had  to  be  varied 
between  20  and  100  volts.  No  harmful  effects  on  the  results 
could  be  detected.]  No  readings  could  be  repeated,  since  the 
alternator  supplying  the  current,  used  to  demagnetize  the  wire, 
was  not  kept  running  at  night.  Two  sets  of  curves  were  taken, 
the  first  when  the  wire  carried  only  the  weight  of  the  apparatus, 
giving  a  tension  of  53  kg.  per  sq.  cm.  in  the  case  of  the  iron,  and 


10 

of  30  kg.  per  sq.  cm.  in  case  of  the  nickel,  the  second  when  the 
load  on  the  wire  was  increased  to  323  kg.  per  sq.  cm.  in  the  iron, 
and  to  179  kg.  per  sq.  cm.  in  the  nickel.  The  temperature  re- 
mained fairly  constant  somewhere  in  the  neighborhood  of  9°  C. 

KESULTS. 

I.  Iron.     Tension  =  53  kg.  per  sq.  cm. 

The  iron  wire  was  one  of  ordinary  commercial  iron,  number 
19  Stubs'  gauge,  diameter  =  .106  cm. 

The  elongations  are  given  in  Table  I  and  plotted  to  //  in  Plate 
I,  and  to  /in  Plate  V.  Values  of  Young's  modulus  are  given  in 
Table  la  and  plotted  to  //in  Plate  I,  and  to  /in  Plate  V.  All 
the  magnetic  quantities  are  given  in  Table  Ib  and  plotted  to  // 
in  Plate  I,  and  to  /  in  Plate  V. 

a.)  Elongation: 

The  elongation  curve  for  the  iron  wire  given  in  Table  aud 
Plate  I  is  the  most  suggestive  of  any  of  those  taken.  It  is 
peculiar  in  showing  an  initial  contraction.  A  glance  at  the  curve 
is  a  much  better  description  than  can  be  put  into  words.  It  will 
be  noticed  that  the  initial  contraction,  while  increasing,  increases 
more  rapidly  than  in  proportion  to  the  magnetizing  force,  and 
reverses  quite  abruptly  at  the  value  of  /fat  which  the  magnetiza- 
tion curve  begins  to  be  convex  upward,  and  at  which  the  perme- 
ability also  changes  abruptly  from  an  increase  to  a  decrease. 
The  length  begins  at  this  point  to  increase  quite  rapidly,  but  less 
than  in  proportion  to  //.  After  regaining  the  original  length, 
the  wire  continues  to  elongate  to  a  maximum,  and  then  contracts 
again  in  the  way  observed  by  Bidwell,  More,  and  others.  This 
curve  is  the  last  and  best  of  four  sets  of  measurements,  which, 
for  various  reasons,  had  to  be  discarded,  but  in  all  of  which  the 
initial  contraction  was  observed. 

This  initial  contraction  can  be  very  satisfactorily  explained  on 
the  well-known  theory  that  particles  of  the  metal  rotate  when 
the  metal  is  magnetized. 

The  last  part  of  this  curve  seems  to  show  that  the  wire  suffers 
a  contraction  directly  proportioned  to  H  after  saturation  is 
reached.  It  has  been  assumed,  therefore,  that  the  change  in 


11 

length  is  equal  to  the  change  produced  by  the  magnetization 
alone,  plus  a  constant  times  H '  •  or,  expressed  in  symbols, 


where  ?  is  the  slope  of  the  straight  part  of  the  curve  and  is 
negative.  To  separate  out  that  part  of  the  elongation  due  to 
the  magnetization  alone  we  have 


If  each  ordinate  of  Table  I  is  increased  by  fH,  we  obtain  Table 
V.  the  results  of  which  are  plotted  in  Fig.  3.  A  relation  between 
elongation  and  magnetization  is  taken  from  this  curve  as  in  Table 
VI  and  plotted  in  Fig.  4. 

b.}  Change  in  Young's  modulus. 

The  points  of  the  curve  are  seen  to  be  a  good  deal  scattered, 
but  serve  well  enough  the  purposes  of  this  paper.  There  is  a 
total  increase  of  about  30%,  the  maximum  being  reached  at 
about  saturation,  followed  by  a  decrease  to  nearly  the  original 
value  at  H  =  100.  A  comparison  between  the  curves  for 
Young's  modulus  and  for  elongation,  seems  to  show  that  they 
are  not  connected. 

II.  Iron.     Tension  =  323  kg.  per  sq.  cm.     Same  wire  as  in  I. 

The  elongations  are  given  in  Table  II  and  plotted  to  ZTin 
Plate  II. 

Values  of  Young's  modulus  are  given  in  Table  Ha  and  plotted 
to  77  in  Plate  II. 

All  the  magnetic  quantities  are  given  in  Table  lib  and  plotted 
to  If  in  Plate  II. 

a.)  Elongation. 

This  elongation  curve  adds  nothing,  except  that  a  small  in- 
crease in  the  tension  of  the  wire  almost  annuls  the  initial  con- 
traction, increases  the  elongation  and  final  contraction. 

b.)  Young's  modulus. 

This,  as  might  be  expected,  shows  a  greater  change  under  the 
increased  load,  the  percentage  increase  being  about  the  same,  but 
the  final  value  only  about  80%  of  the  original  value. 


12 

III.  Nickel     Tension  =  30  kg.  per  sq.  cm. 

Wire  obtained  from  Eimer  &  Amend,  of  New  York.  Number 
15  American  gauge,  diameter  =  .143  cm. 

Elongations  are  given  in  Table  III  and  plotted  to  //in  Plate 
III,  and  to  /in  Plate  VI.  Values  of  Young's  modulus  are  given 
in  Table  Ilia  and  plotted  to  //in  Plate  III, and  to  /in  Plate  VI. 
All  the  magnetic  quantities  are  given  in  Table  III/>  and  plotted 
to  //  in  Plate  III,  and  to  /  in  Plate  VI. 

a.)  Elongation: 

The  wire  increased  in  length,  at  first  more  rapidly,  then  more 
slowly  than  in  proportion  to  the  magnetizing  field,  reaching  a 
maximum  length  just  before  the  point  of  maximum  permeability. 
Contraction  then  began,  soon  bringing  the  wire  to  its  original 
length,  and  continued  much  more  rapidly  than  in  the  iron,  and 
in  proportion  to 'the  magnetizing  force,  until  saturation  \vas  aj. 
preached,  when  the  decrease  in  length  began  to  be  less  than  in 
proportion  to  the  magnetizing  force,  and  so  continued  till  the 
end  of  the  experiment  at  about  //=  300. 

The  curve,  however,  offers  no  opportunity  for  the  separation 
of  the  part  of  the  elongation  due  to  magnetization  alone,  from 
that  part  due  to  the  magnetizing  force. 

/>.)  Young's  modulus. 

The  modulus  curve  shows  an  increase  of  about  '26%  with  the 
maximum  nearly  coincident  with  maximum  elongation,  followed 
by  a  gradual  decrease  to  about  80%  of  its  original  value.  This 
curve,  though  it  suggests  that  the  change  in  Young's  modulus 
may  be  due  to  the  change  in  the  molecular  arrangement,  never- 
theless shows  that  the  change  in  length  is  not  at  all  due  to  the 
change  in  the  modulus.  For  while  an  increase  in  the  modulus 
might  cause  contraction,  it  certainly  could  not  cause  expansion, 
and  similarly,  a  decrease  in  Young's  modulus  might  cause  expan- 
sion, but  not  contraction. 

IV.  Nickel.     Tension  =  179  kg.  per  sq.  cm. 
Same  wire  as  in  III. 

Elongations  are  given  in  Table  IV  and  plotted  to  7/in  Plate  IV. 
Values  of  Young's  modulus  are  given  in  Table  IVa  and  plotted 
to  H  in  Plate  IV. 


13 

All  the  magnetic  quantities  are  given  in  Table  IV b  and  plotted 
to  H  in  Plate  IV.  • 

a.)  Elongation. 

The  small  increase  in  the  tension  of  the  wire  seems  to  cause  a 
decrease  in  the  initial  expansion,  quite  analogous  to  the  decrease 
in  the  initial  contraction  in  the  case  of  iron.  BidwelFs  3d  work 
on  the  effect  of  tension  in  the  contraction  of  nickel  shows  that 
in  strong  fields,  as  the  tension  is  increased,  the  contraction  at 
first  increases  and  then  decreases,  which  is  analogous  to  the  in- 
crease and  subsequent  decrease  in  the  elongation  of  iron  pro- 
duced by  increasing  tension. 

b.}  Young's  modulus. 

The  modulus  curve  does  not  seem  to  be  materially  altered  by 
the  increased  tension. 

DISCUSSION  OF  RESULTS. 

I.  Iron.  The  curves  of  Plate  I  and  Fig.  3  afford  a  striking  veri- 
fication of  Weber's  10  theory  that  the  molecules  of  iron  rotate 
when  magnetized,  which  has  been  elaborated  by  Maxwell  and 
Ewing,  and  indicate  that  this  rotation  is  the  common  cause  of 
both  the  magnetization  and  elongation. 

Thus,  suppose  the  metal  to  be  made  up  of  or  to  contain  small 
particles  of  oblong  shape,  and  magnetized  in  the  direction  of  their 
length.  Take  any  plane  section  of  the  wire  at  right  angles  to  its 
axis :  If  there  is  no  magnetization  of  the  iron,  the  particles  in 
this  section  may  be  supposed  to  be  pointing  in  all  directions, 
thus  magnetically  neutralizing  one  another. 
Now,  suppose  that  all  these  particles,  with 
their  directions  kept  unchanged,  are  moved 
so  that  their  south  poles  coincide.  There 
will  thus  be  formed  a  spherical  pencil  of 
rays,  each  ray  a  small  magnet,  with  the 
south  poles  at  the  center  and  the  north  poles 
in  the  surface,  as  in  the  figure,  where  all 
the  south  poles  are  at  o  and  the  north  poles 
as  at  a,  6,  c,  d.  If  a  magnetizing  force  is  now  applied  in 
the  direction  of  the  arrow,  the  particles,  radii  in  the  figure,  will 


14 

rotate,  as  shown.  If  the  ends  of  the  particles  are  in  some  way 
connected  to  the  metal,  this  rotation  should  produce  a  change  in 
the  thickness  of  the  section  proportional  to  the  sum  of  the 
changes  in  the  cosines  of  the  angles  made  by  the  particles  with 
the  axis. 

For  a  weak  field  the  rotations  should  be  small,  but  those  par- 
ticles that  originally  pointed  downward,  as  o  a,  o  b,  should  turn 
more  than  those  in  the  upper  hemisphere,  since  in  the  lower 
hemisphere  the  turning  moments  increase  as  the  particles  turn, 
while  in  the  upper  hemisphere  they  decrease. 

The  change  in  the  arithmetical  value  of  the  cosines  in  the  lower 
hemisphere  is  negative,  but  of  those  in  the  upper  positive.  Hence 
a  small  magnetizing  force  should  produce  a  contraction  of  the  wire. 
Also,  on  account  of  the  increasing  moments  in  the  lower  hemisphere, 
the  wire  should  contract  more  rapidly  than  in  proportion  to  the 
magnetizing  force,  until  what  might  be  called  the  "average  parti- 
cle," has  passed  the  horizontal  position,  when  the  sign  of  the  change's 
in  length  should  abruptly  reverse,  and  the  wire  elongate,  gradually 
approaching  a  maximum  length  which  should  be  reached  at  satu- 
ration, when  the  particles  are  supposed  to  have  become  parallel. 
If  the  above  is  correct,  it  should  be  possible  to  find  a  connection 
between  the  elongation  and  magnetization  curves.  This  cannot 
be  done,  of  course,  without  knowing  something  not  only  of  the 
shape  of  the  particles,  but,  also,  of  the  law  by  which  they  r« 
turning.  But  a  comparison  between  the  two  curves  can  be  made 
thus :  Consider  the  part  of  the  magnetization  curve  that  is  con- 
cave upward,  i.  e.9  from  H  =  0  to  H  =  2.45.  It  is  evident  that 
before  that  magnetization  is  reached  that  corresponds  to  Jf==  2.45, 
/increases  more  rapidly  than  in  proportion  to  II.  Now,  in  the 
theory  given  above,  each  particle  is  supposed  to  turn  under  the 
influence  of  a  magnetizing  force  and  contribute  to  the  total  mag- 
netization an  amount  proportional  to  the  change  in  the  cosine  of 
the  angle  formed  by  it  with  the  perpendicular.  If  the  particle  is 
below  the  horizontal,  it  will  turn  under  an  increasing  moment, 
and  the  change  in  magnetization,  due  to  it,  will  be  greater  than 
in  proportion  to  the  turning  force.  If  the  particle  is  above  the 
horizontal,  the  change  in  magnetization  due  to  it  will  be  less  than 
in  proportion  to  the  turning  force.  Conversely,  since  the  mag- 
netization up  to  H  =  2.45  increases  more  rapidly  than  in  propor- 


15 

tion  to  the  magnetizing  force,  the  average  motion  of  the  particles 
musi  be  below  the  horizontal.  But  the  contribution  of  each  par- 
ticle to  the  change  in  length,  is  also  given  by  the  change  in  the 
cosine  of  its  angle,  is  negative  if  the  particle  is  below,  positive  if 
above  the  horizontal.  Hence  the  magnetization  curve,  if  plotted 
with  its  sign  changed,  as  far  as  H  =  2.45  should  resemble  the 
elongation  curve  up  to  that  point.  Now  consider  the  magnetiza- 
tion curve  between  H  ==  2.45  and  H  =  2.93.  This  part  is  quite 
straight,  which  shows  that  the  change  in  magnetization  is  pro- 
portional to  the  force,  i.  e.,  that  the  average  motion  of  the  parti- 
cles is  in  the  horizontal.  But  here  the  positive  changes  in  the 
cosine  just  balance  the  negative  changes,  and  we  should  get  no 
change  in  length.  Continuing  from  H  =  2.93  the  magnetization 
curve  is  convex  upward,  showing  that  the  average  motion  of  the 
particles  is  above  the  horizontal.  Hence  the  elongation  curve 
and  magnetization  curve  should  be  similar  beyond  H  =  2.93. 

If  I'  =  the  value  of  I  at  H  =  2.45,  and  I"  the  value  of  I  at 
H=  2.93,  the  comparison  curve  already  carried  to  11=  2. 93  might 
be  continued  from  this  point  by  plotting  ordiuates  equal  to 
I —  I"  —  T.  Now,  the  elongation,  when  the  average  motion  is 
above  the  horizontal,  should  be  very  much  greater  than  the  con- 
traction taking  place  when  the  average  motion  is  below  the  hori- 
zontal, since  in  the  former  case  a  majority  of  the  particles  work 
together.  The  elongation  ordinates  should  be  therefore  prob- 
ably anywhere  from  two  to  five  or  six  times  greater  than  the 
contraction  ordinates.  If  they  are  taken  twice  as  great,  and  the 
comparison  curve  is  continued  from  H '  =  2.93,  by  plotting  ordi- 
nates given  by  2  ( I —  I"}  —  I',  we  get  the  curve  given  in  Table 
VII  and  Fig.  5.  The  similarity  between  this  curve  and  the 
elongation  curve  is  evident  enough  to  make  it  seem  probable 
that  if  we  knew  the  law  by  which  the  particles  resisted  turning, 
we  could,  without  any  guess-work,  construct  from  the  magneti- 
zation curve  one  that  would  approximate  very  closely  to  the 
elongation  curve.  It  seems,  therefore,  that  the  elongation  curve 
of  Plate  I  proves  quite  clearly  that  the  initial  contraction,  elonga- 
tion, and  magnetization  are  all  due  to  the  same  cause,  namely, 
the  actual  rotation  of  particles  in  the  metal. 

The  straight  part  of  the  curve  does  not  seem  to  suggest  any 
specific  positive  conclusion,  except  that  already  given,  that  the 


16 

part  of  the  contraction  not  due  to  the  magnetization  is  pro- 
portional to  H  up  to  a  certain  limit.  Some  negative  conclu- 
sions, however,  are  quite  evident.  The*  strain  in  the  metal  pro- 
duced by  the  magnetic  field,  after  saturation,  cannot  be  like  an 
ordinary  mechanical  one,  for  since,  within  the  elastic  limit,  strains 
are  proportional  to  stresses,  the  curve  should  continue  straight  for 
the  strongest  fields  attainable  with  a  solenoid,  or  if  it  curved  at 
all  it  should  be  concave  downward.  Bidwell  has  shown1"1,  how- 
ever, that  after  a  certain  strength  of  field  has  been  passed,  the 
contraction  is  less  than  in  proportion  to  the  field,  and  for  the 
specimen  he  used,  ceased  entirely  at  about  //  =  1250,  the  curve 
beyond  this  point  being  horizontal.  To  conclude,  therefore,  the 
initial  contraction  and  subsequent  elongation  may  be  explained 
as  due  to  the  rotation  of  particles  in  the  iron,  and  the  final  con- 
traction, whatever  may  be  its  cause,  is  not  an  ordinary  mechani- 
cal strain,  and  is  not,  as  one  would  expect  from  the  equations  of 
Maxwell,  and  from  experiments  on  magnetic  tractive  force",  pro- 

J52 

portional  to  &—  . 

o~ 

The  effects  of  a  small  increase  in  tension,  upon  the  elongation 
due  to  magnetization,  as  shown  in  Plate  II,  namely,  decrease  in 
the  initial  contraction  and  increase  in  the  elongation,  are  what 
one  would  expect,  if  there  is  any  looseness  of  the  particles,  as 
must  be  the  case,  if  they  can  rotate.  It  is,  however,  hard  to  see 
why  tension  should  increase  the  final  contraction. 

II.  Nickel: 

The  explanation  of  the  elongation  curves  for  nickel,  Plates  III 
and  IV,  is  not  so  easy  as  in  the  case  of  the  iron. 

If  the  particles  were  flattened  instead  of  elongated,  in  the 
direction  of  their  magnetic  axes,  their  rotation  would  combine  with 
the  contraction  proportional  to  the  field  to  make  up  the  curve  as 
far  as  £T=  90.  Since,  however,  the  ultimate  effect  of  the  rota- 
tion would  be  contraction,  and  what  might  be  called  the  magnetic 
elastic  limit,  is  approached  so  early,  it  would  be  impossible  to 
separate  out  the  change  due  to  the  rotation  alone,  for  compari- 
son with  the  magnetization  curve. 

The  effects  of  a  small  increase  in  the  tension  of  the  wire, 
namely,  decrease  in  the  initial  expansion,  and,  according  to  Bid- 


well,  increase  in  the  final  contraction,  seem  to  complete  the  analogy 
between  the  phenomena  shown  by  iron  and  nickel,  provided  the 
particles  of  the  latter  are  flattened  in  the  direction  of  their  mag- 
netic axes. 

DISCREPANCIES  BETWEEN  THESE  RESULTS  AND  THOSE  OF  OTHERS.    . 

In  the  case  of  iron,  it  has  been  impossible  to  find  in  the  work 
of  other  investigators,  any  mention  of  an  initial  contraction,  like 
that  shown  in  Table  and  Plate  I. 

Similarly  in  the  case  of  nickel,  it  has  been  impossible  to  find 
any  record  of  an  initial  elongation  like  that  shown  in  Table  and 
Plate  III.  In  the  figures  given  by  More,  in  his  work  on  iron, 
the  weakest  field  used  is  4.6,  at  which  strength  of  field,  tke  iron 
wire  of  Plate  I  has  more  than  regained  its  original  length. 
It  is,  however,  hard  to  see  why  these  initial  effects  are  not  re- 
corded in  the  extensive  work  of  Bidwell.  Many  of  his  tables 
show  initial  fields  weak  enough  to  produce  the  initial  contraction 
in  iron,  and  initial  expansion  of  nickel. 

His  remarks  on  the  peculiarities  shown  by  annealed  speci- 
mens ;if  of  iron,  suggest  that  the  annealing  to  which  the  speci- 
mens examined  in  this  paper  were  subjected,  put  them  in  a  con- 
dition to  show  the  unusual  initial  effects,  and  that  if  Bidwell  had 
given  more  attention  to  his  annealed  specimens,  and  examined 
them  with  weaker  fields  and  lighter  loads,  the  initial  contraction 
of  iron,  and  expansion  of  nickel,  would  not  have  escaped  his 
notice. 

The  results  for  iron,  shown  in  Tables  and  Plate  I,  are  also 
shown  in  Plate  V,  but  plotted  to  magnetization  instead  of  mag- 
netizing field.  The  great  differences  between  the  elongation 
curve  and  the  unconnected  curve  of  Dr.  Moie,  already  given,  are 
obvious,  and  illustrate  what  variations  may  be  shown  by  two 
different  specimens,  though  studied  with  the  same  apparatus. 
Plate  V  shows  better,  perhaps,  than  Plate  I  how  greatly  the 
change  in  length  is  affected  by  the  magnetizing  field,  after  the 
change  due  to  the  magnetization  has  practically  ceased.  Plate 
VI  shows  the  results  for  nickel  of  Tables  and  Plate  III,  plotted 
to  I  instead  of  //,  but  does  not  seem  to  throw  any  additional 
light  upon  the  matter. 


18 


SUMMARY  OF  RESULTS. 

Iron.     Phenomena  observed. 

1.  The  wire  showed  an  initial  contraction  when  magnetized, 
contracting  more  rapidly  than  in  proportion  to  the  magnetizing 
field.     At  about  the  point  where  the  magnetization  increases 
most  rapidly  and  the  permeability  is  greatest,  this   contraction 
ceased  and  the  wire  began  to  expand  more  slowly  than  in  pro- 
portion to  the  magnetizing  field,  till  a  maximum  length  was 
reached  in  the  neighborhood  of  saturation.     The  wire  then  con- 
tracted in  direct  proportion  to  the  magnetizing  field,  up  to  //  = 
250,  where  the  experiment  was  brought  to  an  end. 

2.  The  instantaneous  modulus  of  elasticity  was  found  to  in- 
crease over  30%,  reaching  a  maximum  at  saturation,  but  de- 
creased again  to  nearly  its  original  value  at  about  //=  300. 

3.  A  small  increase  in  the  tension  of  the  wire  reduced  the 
initial  contraction,  did  not  appreciably  change  the  percentage 
increase  in  the  modulus,  but  the  final  decrease  in  the  modulus 
left  it  at  only  about  80%  of  its  original  value. 

CONCLUSIONS. 

1.  The  initial  decrease  in  the  length  of  the  wire  and  the  elon- 
gation, are  explained  as  due  to  the  rotation  of  particles  in  the 
metal. 

2.  The  final  contraction  is  not  an  ordinary  mechanical  strain, 

is  not  proportional  to  ^-  ,  but  is  proportional  to  the  magnetiz- 

O/T 

ing  field. 

3.  The  change  in  the  modulus  seems  to  have  nothing  to  do 
with  the  change  in  length. 

Nickel.     Phenomena  observed. 

1.  The  nickel  wire,  when  magnetized,  increased  in  length,  at 
first  more  rapidly,  then  more  slowly  than  in  proportion  to  the 
magnetizing  field,  reaching  a  maximum  length  just  before  the 
point  where  the  permeability  was  greatest.  Contraction  then 
began,  soon  bringing  the  wire  to  its  original  length,  and  con- 


19 

tinued  much  more  rapidly  than  in  the  iron,  and  in  proportion  to 
the  magnetizing  force,  until  saturation  was  approached,  when 
the  decrease  in  length  began  to  be  less  than  in  proportion  to  the 
magnetizing  force,  and  so  continued  till  the  experiment  was  ended 
at  about  H  =  300. 

2.  The  instantaneous  modulus  of  elasticity  increased  about 
26%,  reaching  a  maximum  at  about  the  same  field  as  that  of  the 
maximum  elongation,  and  then  fell  to  80%  of  its  original  value 
at  about  //==  300. 

3.  A  small  increase  in   the   tension   of  the  wire  reduced   the 
original  expansioD,  the  increase  in  the  modulus  was  about  23%, 
and  its  final  value  88%  of  its  original  value. 

CONCLUSIONS. 

1.  The  results  for  nickel  are  not  so  easily  explained  as  those 
for  iron.     They  do  not,  however,  conflict  at  all  with  those  for 
iron,  but   confirm,   though   not  very  definitely,  the   conclusions 
drawn  therefrom. 

2.  The  change  in  the  modulus  does  not  seem  to  have  anything 
to  do  with  the  change  in  length. 


I  ought  to  say  that  the  conclusions  drawn  in  this  paper  are 
entirely  my  own,  and  must  not  be  taken  as  involving  the  opinion 
of  any  one  connected  with  this  University. 

In  closing,  I  would  express  most  hearty  thanks  to  Dr.  Ames 
for  his  kindness  and  help  throughout  this  work,  and  to  Prof. 
Eowland  for  his  consideration  and  suggestions. 

EDSON  F.  GALLAUDET. 

JOHNS  HOPKINS  UNIVERSITY,  May,  1896. 


TABLE  I. — Iron. 
Tension  in  wire  =  53  kg.  per  sq.  cm. 


H 

^xlO> 

H 

£xir 

z  x  10" 

1.1 

—       3.99 

11.70 

57.91 

66.29 

5.99 

1.64 

6.66 

13.58 

58.57 

82.74 

—     20.63 

2.24 

10.65 

14.52 

58.57 

94.63 

43.93 

3.02 

—    21.30 

17.33 

58.57 

105.60 

—     63.23 

3.34 

—    20.63 

18.51 

58.57 

118.86 

-     89  .  86 

3.66 

13.98     i 

23.31 

58.57 

136.23 

—  124.47 

3.93 

7.32 

27.84 

57.24 

158.17 

-  171.06 

4.20 

—         .67 

33.00               54.58 

191.10 

-  236.3 

6.35 

-f    32.62 

36.75               51.25 

224.46 

—  299.53 

7.22 

39.27 

41.33 

45.93 

251.43 

—  352.78 

8.91 

47.92 

46.95 

37.27 

10.29 

53.92 

54.86 

25.96 

TABLE  la. 
Values  of  the  modulus  of  elasticity. 


* 

*L  x  1019  =  M 

al 

H 

7Y'X  10ia=Jf 

ill 

H 

^x  10"=  M 
al 

2.89 

2.79 

26.57 

3.37 

128.00 

3.72 

4.02 

2.7!) 

41.28 

3.40 

150.04 

3.80 

4.98              2.84 

47.13 

3.47 

165.49 

3.<J4 

6.81 

2.90 

56.14 

3.52 

179.66 

3.55 

9.05 

2.96 

65.56 

3.62 

205.26 

3.52 

11.34 

3.12 

73.60 

3.62 

211.20 

3.35 

13.81 

3.23 

84.12 

3.72 

256.00 

3.34 

15.91 

3.24 

91.89 

3.65 

301.72 

3.07 

18.38 

3.24 

109.26 

3.62 

21.58 

3.37 

11'.).  77 

3.74 

21 


TABLE  Ib. 


H 

B 

!•>• 

/ 

H 

B 

/>• 

1 

.9 

193 

214 

15.3 

22.83 

15351 

672 

1220 

1.2 

268 

223 

21 

28.89 

15565 

539 

1236 

1.5 

367 

245 

29 

34.41 

15840 

460 

1258 

1.8 

516 

287 

41 

38.4 

16002 

417 

1270 

2 

6G3 

331 

53 

41.37 

16021 

387 

1272 

2.2 

900 

409 

71 

47  64 

16175 

340 

1283 

2.3 

1087 

473 

86 

52.71 

16334 

310 

1296 

2.4 

1446 

603 

115 

60.44 

16514 

273 

1309 

2.51 

2835 

3129 

225 

64.73 

16586 

256 

1315 

2.7 

5554 

2057 

442 

68.57 

16630 

243 

1319 

2.826 

7571 

2679 

602 

74.97 

16873 

225 

1337 

3.2 

10641 

3325 

847 

81.14 

16880 

208 

1337 

4.43 

12437 

2808 

989 

89.60 

17115 

191 

1335 

5.49 

13288 

2421 

1057 

99.66 

17374 

174 

1375 

6.86 

13815 

2014 

1099 

125.26 

17841 

142 

1410 

8.14 

14058 

1727 

1118 

151.09 

18280 

121 

1443 

10.06 

14393 

1431 

1145 

178.23 

18329 

103 

1444 

12.43 

14651 

1179 

1165 

205,03 

18793 

92 

1479 

15.54 

14905 

959 

1185 

228.57 

18942 

83 

1489 

19.02 

15217 

800 

1209 

299.44 

19571 

65 

1534 

TABLE  II. 
Wire  under  tension  of  323  kg.  per  sq.  cm. 


H 

«x» 

Lt 

H 

^xlO- 

Ll 

H 

%*» 

1.05 

.67 

10.93 

72.55 

69.94 

—     17.97 

1.23                    .67 

12.75 

72  .  55 

80.46 

—     38.61 

1.51                  1.33 

14.31 

75.21 

100.12 

79.21 

1.87 

—       1.33 

16.09 

73.88 

110.17 

-  103.84 

2.51 

-f    32  62 

18.70 

64.56 

124.80 

—  137.12 

3.11 

59.90 

... 

57.91 

142.63 

-  181.71 

3.70 

65.23 

29.  '53 

56.58 

166.40 

-  235.62 

4.30 

69.89 

35.89 

44.60 

201.15 

-  312.17 

5.94 

71.22 

40.00 

41.27 

246.86 

-  392.05 

6.35 

69.89 

45.72 

28.62 

269.72 

—  445.30 

7.45 
9.14 

69.89 
72.55 

53.76 
64.41 

17.31 
—       3.99 

f 

22 


TABLE  Ha. 
Values  of  modulus  of  elasticity. 


H 

^  x  10"  =  M 

al 

H 

^x!0»=Jf 

H 

^x  10"  =  M 
al 

2.88 

7.74 

33.28 

10.47 

113.38 

11.56 

3.66 

9.44 

36.98 

10.33               121.60 

10.46 

5.03 

9.68 

44.25 

11.06 

131.66 

10.06 

7.45 

9.33 

52.62 

10.76 

143.09 

10.06 

9.13 

9.00 

58.47 

11.39 

157.26 

8.60 

12.02 

9.68 

65.24 

11.91 

174.64 

8.60 

15.04 

9.68 

68.57 

11.73 

197.49 

7  67 

18.38 

9.68 

79.09 

11.91 

211.66 

7.74 

23.64 

9.68 

85.94 

12.49 

237.72 

8.15 

27.93 

9.80 

103.05 

12.10 

301.73 

7.45 

TABLE  Ub. 


H 

B 

/* 

I 

H 

B 

/J- 

/ 

.8 

168 

210 

13.3 

12.71 

14(599 

1157 

1169 

1 

214 

214 

17 

15.77 

14892 

944 

1184 

1.3 

293 

225 

23 

20.43 

15197 

744 

1208 

1.5 

353 

235 

28 

27.02 

15552 

576 

1235 

1.7 

429 

252 

34 

31.91 

156HO 

491 

1245 

1.9 

524 

276 

42 

39.27 

15799 

402 

1254 

2.1 

666 

317 

53 

48.92 

16174 

331 

1283 

2.3 

962 

418 

76 

55.43 

16267 

293 

1990 

2.42 

1824 

754 

145 

66.04 

16433 

249 

1302 

2.70 

5952 

2204 

473 

75.43 

16545 

219 

1311 

2.88 

8106 

2815 

645 

91.43 

16954 

185 

1342 

3.11 

10858 

3491 

864 

116.57 

17417 

149 

1377 

3.22 

11901 

3696 

947 

141.72 

17852 

126 

1409 

4.57 

13093 

2865 

1042 

172.57 

18148 

105 

1430 

6.33 

1M905 

2197 

1106 

215.32 

18607 

86 

1464 

7.8*4 

14162 

1806 

1126 

222.86 

18872 

85 

1484 

10.38 

14561 

1403 

1158 

297.15 

19420 

65 

1522 

23 


TABLE  III.— Nickel. 
Tension  in  wire  =  30  kg.  per  sq.  cm. 


fir 

H 

^  x  10* 
J.J 

H 

77  x  1Q8 

H 

z  x  1Q8 

.59 

.67 

11.02 

46.59 

64.37 

—  679.59 

.78 

.67 

12.89 

51.92 

70.40 

—  779.44 

1.05 

1.33 

14.22 

52.58 

87.77 

992.43 

1.37 

2.00 

16.23 

48.59 

101.94 

-  1152.2 

2.10 

6.00 

18.83 

35.28 

119.32 

-  1333.2 

3.38 

12.65 

22.26 

1  33 

146.74 

—  1660.7 

4.57 

18.64 

27.29 

—  60.57 

170.52 

-  1848.4 

5.12 

19.97 

32.50 

—  133.79 

^06.17 

—  2061.4 

5.48 

21.30 

35.89 

—  185.71 

242^29 

-  2234.5 

6.35 

26.63 

42.97 

-  320.16 

315.44 

—  2488.7 

7.54 

33.28     49.69 

-  433.32 

9.23 

41.27     58.52 

—  566.44 

TABLE 
Values  of  the  modulus. 


H 

^x  IQ11  =  M 

TT 

^x!0"  =  Jf 

H 

-f  x  10n  =  M 

al 

al 

al 

0 

6.92 

13.71 

8.65 

100.11 

7.50 

.23 

7.40 

18.20 

8.72 

116.57 

7.80 

1.01 

7.53 

23.68 

8.55 

139.89 

7.36 

1.69 

7.87 

32.18 

8.40 

175.09 

5.94 

2.38 

7.97 

39.41 

8.33 

211.20 

6.09 

3.29 

8.17 

45.53 

8.22 

233.15 

6.04 

4.21 

8.28 

52.94 

8.36 

278.86 

5.76 

5.99 

8.43 

63.96 

8.25 

329.15 

5.64 

7.41 

8.51 

69.94 

8.17 

10.15 

8.65 

84.57 

7.72 

TABLE  III&. 


H 

B 

V 

/ 

H 

B 

> 

1 

1 

24 

24 

1.8 

31.91 

2711 

85 

213 

2 

48 

24 

3.6 

37.58 

2997 

80 

236 

3 

74 

25 

5.6 

45.99 

3362 

73 

264 

4 

105 

26 

8 

54.86 

3662 

67 

278 

5 

149 

30 

11.4 

66.88 

3969 

59 

311 

5.5 

174 

32 

13.4 

77.26 

4245 

55 

332 

6.13 

246 

40 

19 

97.83 

4556 

47 

355 

6.99 

293 

42 

23 

129.37 

4942 

38 

383 

8.23 

405 

49 

32 

142'.  4 

5064 

36 

392 

9.28 

485 

52 

38 

173.49 

5305 

31 

408 

10.65 

604 

57 

47 

212.12 

5495 

26  !   420 

15.22 

1220 

80 

96 

221.20 

5635 

25     431 

20.8 

1882 

91 

148 

242.29 

5633 

23 

429 

25.69 

2313 

90 

182 

290.29 

6787 

L>0 

437 

TABLE  IV. 
Wire  under  tension  of  179  kg.  per  sq.  era. 


H 

^xlO< 
_// 

H 

%xIO- 

H 

¥*>»' 

.23 

.67 

9.10 

23.96 

67.89 

—    7",7.r, 

.73 

.67                12.98 

19.30 

87.77 

-  1052.3 

1.14 

2.00                 16.32 

4.66 

121.14 

—  1398.5 

1.83 

6.66                 20.62 

34.61 

148.57 

-  1667.4 

2.83 

8.65                 27.-J-.I 

114.49 

181.95 

-  1940.3 

3.61 

10.65 

30.03 

170.4 

212.12 

—  2149.9 

4.53 

12.65 

37.17 

—     278.9 

242.29 

—  2372.3 

5.99 

17.97 

45.30 

397.4 

288 

—  2579.9 

7.04 

21.30 

57.56 

—    579.1 

25 


TABLE  IVa. 


Values  of  the  modulus. 


TJ  r 

H 

al 

H 

^x  1012=  M 

al 

H 

1  ,    x  1012  =  M 

al 

0 

3.38 

4.98 

4.09 

66.97 

3.73 

.46 

3.49 

6.17 

4.09 

78.17 

3.35 

.91 

3.67 

7.86 

4.05 

86.40 

3.55 

1.37 

3.87 

9.28 

4.21 

109.26 

3.11 

1.83 

3.97 

11.89 

4.17 

134.86 

3.30 

2.29 

3.90 

14.54 

4.29 

156.35 

3.11 

2.74 

4.01 

18.24 

4.52 

192.00 

3.30 

3.20 

4.09 

30.04 

4.09 

223.55 

3.30 

3.66             4.13 

40.46 

3.90 

274.29 

2.84 

4.11              4.13 

53.21 

3.55 

TABLE  IVft. 


H 

13 

1J- 

/ 

H 

B 

/->- 

/ 

2 

52 

26 

4 

18.29 

1451 

79 

114 

3 

80 

27 

6.1 

22.86 

1866 

82 

147 

4 

117 

29 

9 

32.69 

2479 

76 

195 

5 

159 

32 

12.2 

40.69 

2860 

70 

224 

6 

207 

35 

16 

49.69 

3209 

65 

251 

6.86 

253 

37 

19.6 

59.34 

3501 

59 

274 

7.77 

333 

43 

26 

73.6 

3887 

53 

303 

8.69 

397 

46 

31 

87.32 

4185 

48 

326 

10.06 

484 

48 

38 

97.37 

4357 

45 

339 

10.97 

564 

51 

44 

116.34 

4530 

39 

351 

11.89 

676 

57 

53 

143.09 

4945 

35 

382 

12.8 

788 

62 

62 

192.46 

5330 

28 

409 

14.63 

1036 

71 

81 

240 

5564 

23 

424 

16 

1196 

75 

94 

333.72 

5904 

18 

443 

26 


TABLE  V. 
Elongations  of  Table  I  due  to  magnetization  alone. 


—  1.98. 


H 

-^  x  10" 

^  x  io8  +  rn 

H 

XXl°8 

^  x  10"  +  /-// 

L 

L 

1.1 

—   3.99 

—    1.81 

23.21 

58.57 

104.80 

1.65 

—   6.66 

—    3.40 

27.84 

57.24 

112.45 

2.24 

10.65 

6.21 

33.00 

54.58 

120.03 

3.02 

21.30 

—   15.31 

36.75 

51.25 

124.13 

3.34 

—  20.63 

—   14.01 

41.33 

45.93 

127.90 

3.66 

—  13.98 

—    6.72 

46.95 

37.27 

130.38 

3.93 
4.20 

—   7.32 
.67 

+     .47 
4-    7.66 

54.86 
66.29 

25.96 
5.99 

134.76 
137.46 

6.35 

+  32.62 

45.21 

82.74 

20.63 

143.46 

7.22 

39.27 

53.59 

94.63 

—  43.93 

143.75 

8.91 

47.92 

65.59 

105.60 

—  63.23 

146.20 

10.29 

53.92 

74.33 

118.86 

—  89.86 

145.87 

11.70 

57.91 

81.11 

136.23 

-  124.47 

145.71 

13.58 

58.57 

85.50 

158.17 

-  171.06 

142.63 

14.52 

58.57 

87.37 

191.10 

—  236.30 

142.70 

17.33 

58.57 

92.94 

224.46 

—  299.53 

145.63 

18.51 

58.57 

95.28 

251.  4:j 

—  352.78 

145.86 

I 

TABLE  VI. 


/ 

?«.» 

7 

^xlO« 
Li 

/ 

«»„ 

20 

—   2 

560 

—  12 

1180 

88 

40 

—   4 

710 

—  14 

1220 

103.2 

70 

—   6 

770 

—  15.5 

1258 

121.6 

100 

—   7.2 

840 

—  16.8 

1296 

134.2 

130 

—   7.6 

870 

—  14.7 

1337 

141.1 

160 

—   7.8 

910 

—   8 

1360 

144 

190 

—   8 

950 

0 

1400 

144.2 

220 

—   8.4 

1000 

14 

1534 

144.2 

330 

—   9.4 

1060 

34 

450 

—  10.5 

1100 

52 

27 

TABLE  VII. 


H 

a  =  —I 

H 

a  =  2  (I—  I")  —  I' 

1 

—    18 

1 

650 

1.5 

24 

11.8 

770 

2 

53 

16.5 

830 

2.3 

86 

19 

868 

2.45 

—   150 

40 

990 

... 

a  =  2(7—  I"}  —  I' 

100 

1180 

2.93 

150 

180 

1350 

3.04 

10 

3.2 

"  130 

3.6 

270 

r  =  iso 

4.5 

450 

/"  =  700 

28 


PLATES  AND  DIAGRAMS. 

Plate      1.     Iron.     Curves  of  change  in  length,  magnetization,  permeability, 

induction,  and  Young's  modulus,  all  plotted  to  H. 
Tensile  stress  —  53  kg.  per  sq.  cm. 

Plate      I.     Enlarged.     Enlargement  of  first  part  of  elongation  and  magne- 
tization curves  of  Plate  I. 
Plate    II.     Iron.     Curves  of  change  in  length,  magnetization,  permeability, 

induction,  and  Young's  modulus,  plotted  to  H. 
Tensile  stress  =  323  kg.  per  sq.  cm. 
Plate  III.     Nickel.     Curves  of  change  in  length,  magnetization,  induction, 

permeability,  and  Young's  modulus,  plotted  to  H. 
Tensile,  stress  =  30  kg.  per  sq.  cm. 
Plate  IV.     Nickel.     Curves  of  change  in  length,  magnetization,  induction, 

permeability,  and  Young's  modulus,  plotted  to  H. 
Tensile  stress  =  179  kg.  per  sq.  cm. 

Plate    V.     Iron.     Curves  of  change  in  length,  permeability,  Young's  mod- 
ulus, and  magnetizing  field,  plotted  to  /. 
Tensile  stress  =  53  kg.  per  sq.  cm. 
Plate  VI.     Nickel.     Curves  of  change   in   length,   permeability,    Young's 

modulus,  and  magnetizing  field,  plotted  to  /. 
Tensile  stress  =  30  kg.  per  sq.  cm. 
Figure  3.     Iron.     Curve  of  change  in  length  due  to  magnetization  alone, 

plotted  to  H. 

Tensile  stress  =  53  kg.  per  sq.  cm.     First  part  enlarged. 
Figure  4.     Iron.     Curve  of  change  in  length  due  to  magnetization  alone, 

plotted  to  magnetization. 
Tensile  stress  =  53  kg.  per  sq.  cm. 

Figure  5.  Comparison  curve,  constructed  from  magnetization  curve  of 
Plate  I,  and  plotted  to  H,  showing  similarity  to  elongatian 
curve  of  Fig.  3. 


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REFEBENCES. 


1.  Barrett,     a)  Nature  1882,  Vol.  26,  p.  585. 

b)  Phil.  Mag.  1874,  Vol.  47,  p.  51. 

2.  Berget.     Comp.  Rend.  1892,  Tom.  115,  p.  722. 

3.  Bidwell.     a)  Proc.  Roy.  Soc.  1885,  Vol.  38,  p.  265. 

b)  "         " "       "    1886,  Vol.  40,  pp.  109,  257. 

c)  "         "         "    1888,  Vol.  43,  p.  407. 
d}      "         "         "    1890,  Vol.  47,  p.  469. 
e)      "         "         "    1892,  Vol.  51,  p.  495. 

/)      "         "      '  "    1894,  Vol.  55,  p.  228. 
g}      "         "         "    1894,  Vol.  56,  p.  94. 
h)  Phil.  Tran.  Roy.  Soc.  1888,  Vol.  179A,  p.  205. 

4.  Bock.     Wied.  Ann.  1895,  Vol.  54,  p.  442.     ' 

5.  Chree.     a)  Phil.  Tran.  Roy.  Soc.  1890,  Vol.  181,  p.  339. 

b)  Nature  1896,  Vol.  53,  p.  269,  365,  533. 

6.  Jones,     a)  Phil.  Mag.  1895,  Vol.  39,  p.  254. 

b)      "         "     1896,  Vol.  41,  pp.  153,  454. 

7.  Joule.     Phil.  Mag.  1847,  Vol.  30,  p.  76,  225. 

8.  Knott.     Phil.  Mag.  1894,  Vol.  37,  p.  141. 

9.  Lochner.     Phil.  Mag.  1893,  Vol.  36,  p.  498. 

10.  Maxwell.     Elec.  and  Mag.  Vol.  2,  Chap.  6. 

11.  Mayer,     a)  Phil.  Mag.  1873,  Vol.  45,  p.  350. 

b)      "         "     1873,  Vol.  46,  p.  177. 

12.  More.     Phil.  Mag.  1895,  Vol.  40,  p.  345. 

13.  Nagaoka.     a)  Phil.  Mag.  1894,  Vol.  37,  p.  131. 

b)  "         "     1896,  Vol.  41,  p.  454. 

c)  Wied.  Ann.  1894,  Vol.  53,  p.  487. 

14.  Mary  C.  Noyes.     Physical  Review  1896,  Vol.  3,  p.  432. 

15.  J.  J.  Thomson.     Appl.  Dyu.  to  Ph.  and  Chem. 


BIOGRAPHICAL  SKETCH. 

Edson  Fessenden  Gallaudet  was  born  at  Washington,  D.  C., 
April  21,  1871.  Entered  the  Hartford  Public  High  School  in 
1885,  graduating  in  1889.  In  fall  of  that  year  entered  Yale  Uni- 
versity, in  the  Academic  Department ;  graduated  in  1893.  In  fall 
of  1893  entered  upon  graduate  work  at  Johns  Hopkins  Univer- 
sity, where  he  studied  till  June,  1896.  Best  known  as  the  second 
son  of  E.  M.  Gallaudet,  President  of  the  Columbian  Institution 
for  the  Deaf  and  Dumb,  Washington,  D.  C. 


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